Franken had been engaged in a months-long legal fight over the validity of the November 4 election.
A series of recounts in the state gave him a victory of just 312 votes over Coleman, prompting the Republican to challenge the accuracy of the recount.
Coleman has the option to appeal the decision to the US supreme court.
Should Franken be seated, Democrats would possess the 60 senate votes needed to prevent opponents from forcing a filibuster, a tactic which delays the passage of legislation through parliament through the method of protracted debate.
Further control of the senate would give Barack Obama, the US president, increased power to advance his legislative agenda.
The Democrats already have a strong majority in the House of Representatives, the lower house of the US’ bicameral legislature.